melissa
student
this question is secondary level
Q:(involes with related rates)
A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
please help i'm not even sure how to set up the picture for this problem?
Hi Melissa,
I drew the diagram below. L is the lighthouse, P is the closest point on the shoreline and S is the spot where the light hits the shoreline. L and P are fixed but S moves as the light rotates.
I labeled the angle PLS as theta and the changing length |SP| as x.
Since the light makes 4 revolutions per minute theta changes 4(2 pi) = 8 pi radians every minute. Hence 
radians per minute.
From the diagram the tangent of theta is x/3. Can you complete the problem now?
Penny